Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Cherednik I. — Double Affine Hecke Algebras
Cherednik I. — Double Affine Hecke Algebras



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Double Affine Hecke Algebras

Автор: Cherednik I.

Аннотация:

This is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, for those who want to master the new double Hecke algebra technique.


Язык: en

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 434

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$E_b, \mathcal E_b$: nonsym polynomials      314
$e_n$, $\varepsilon_n$: nonsym polynomials      197
$P_b, p_n$: sym polynomials      93 316
$s_i$: simple reflections      1—417
$\alpha_i$, simple roots      1—417
$\eta$ involution      202 308
$\heartsuit$ anti-involution      318 330 397
$\lambda$ half-singular ($A_1$)      238
$\lambda$ regular ($A_1$)      238
$\lambda$ singular ($A_1$)      238
$\mathbb C$: complex numbers      1—417
$\mathbb N$: natural numbers      1—417
$\mathbb Q$: rational numbers      1—417
$\mathbb R$: real numbers      1—417
$\mathbb S_n$: permutation group      1—417
$\mathbb Z$: integers      1—417
$\mathbf H_n$: nonaffine Hecke      100 359 367
$\mathcal P$: polynomial rep      1—280
$\mathcal V$: polynomial rep      372—417
$\mathcal{HH}', \mathcal{HH}''$      120 190 277
$\mathcal{HH}, \mathcal{HH}_n, \mathcal{HH}^\flat$      100 306 311
$\mathcal{H}'_\Sigma, \mathcal{H}'$      54 109
$\mathcal{H}, \mathcal{H}_X, \mathcal{H}_Y$      61 312
$\mathfrak F$, F      326 383
$\phi$ anti-involution      95 200 318
$\Phi$: solution of KZ, QKZ      1—153
$\Phi_{\hat w}, S_{\hat w}, G_{\hat w}$: intertwiners      281—417
$\pi_r$: elements from $P^\vee/Q^\vee$      1—117
$\rho$      294 306
$\sigma$ automorphism      213 272 307
$\Sigma$: root system      1—153
$\star$ anti-involution      308
$\tau$-function      45
$\tau$—function (r—matrix)      136
$\tau_\pm$ automorphisms      272 307
$\tilde W, \hat W$: affine Weyl groups      295
$\varepsilon$ involution      213 272 307
$\varphi$: solution of QMBP      1—153
Additional series ($A_1$)      231 233 251
Affine action (wb)((z))      300
Affine Hecke algebra $\mathcal H$      61 312
Affine KZ equation ($A_1$)      48
Affine pairing ($[z, l], z'+d$)      300
Affine quantum KZ ($GL_n$)      78
Affine r-matrix      112
Affine root system      118 295
Affine Weyl chamber $\mathfrak C^a$      119 300
Affine Weyl chamber $\overline{\mathfrak C}^a$      125
Affine Weyl group $tilde W$      112 295
Affine Weyl group $\hat W$      112 262 295
Affine Weyl group $\hat{\mathbb S}_n$      79
AKZ      48 52 55
Anti-involution $\phi$      95 200 318
Anti-involution $\phi, GL_n$      102
Anti-involution $\star$      308
Anti-involution trivial      57
Anti-involution X-trivial      380 383
Appell function A(k, r)      182
AQKZ      78
Asymptotically free solution      63
Automorphism $\sigma$      213 272 307
Automorphisms $\tau_\pm$      272 307
Baker function $\varphi$      151
Basic hypergeometric function      161
Baxter — Belavin r-matrix      151
Baxterization (affine)      90
Bilinear form (*-bilinear)      314
Boundary of $\delta$      360
Braid group (elliptic)      216
Braid group (pure)      104
Braid group (universal)      413
Category $\mathcal O$      343
Central extension $\hat{\mathfrak g}$      132
Central extension ($PGL(2, \mathbb Z)$)      392
Chain (integral formulas)      143
Characteristic functions $\chi_m$      221
Characteristic functions $\chi_{\hat\omega}$      327
Coinvariant $\pi$ (KZB)      153
Coinvariant $\pi(\hat{\mathfrak g})$      138
Coinvariants $\varpi$ (DAHA)      371 372
Commutativity relations (Hecke)      77
Compact case      164
Component of a diagram      143
Composition of paths      60 217
Conjugation on polynomials      199
Constant term CT      168
Constituents of $\mathcal I_\xi$ (DAHA)      385
Convex set of roots      302
Coroot $\alpha^\vee$      262
Cospherical forms $\varpi$      371 372
Cospherical module (DAHA)      371
Coxeter number h      339
Coxeter relations (Hecke)      61 77
Creation operator ($A_1$)      197
Cross-relations (Hecke)      77
Cutoffs      68
Cyclic module (X, Y)      344 345
DAHA      100 120 306
Definite form for X, Y      345 346
Degenerate DAHA $\mathcal{HH'}$      120 274
Degenerate DAHA $\mathcal{HH}''$      190 277
Degenerate DAHA $\mathcal{HH}_0'$      115
Degenerate Hecke algebra $\mathcal H'$      53 109
Degenerate Hecke algebra $\mathcal H'_n$      52
Degenerate Hecke algebra $\mathcal H'_{A_1}$      49
Delta functions $\delta_m$ ($A_1$)      221
Delta functions $\delta_{\hat w}$      327
Delta-representation $\Delta$      383
Demazure — Lusztig operators $S_i$      122
Demazure — Lusztig operators $\hat T_i$      310
Diagonal coinvariants      279 412
Diagram $\delta$ (generalized)      369
Diagram $\delta$ (periodic)      360 362
Diagram (integral formulas)      143
Discretization $\delta$ (DAHA)      326
Discretization ($A_1$)      97 213
Double Hecke algebra      100 120 306
Double Hecke algebra ($A_1$)      95 198
Double Hecke algebra ($GL_n$)      100 357
Double Hecke algebra (rational)      277
Double Hecke universal      414
Duality formula ($A_1$)      94 200
Duality formula ($GL_n$)      99
Duality formula (DAHA)      318 396
Dunkl operators (difference)      122 273
Dunkl operators (infinite)      113
Dunkl operators (no shifts)      71 111
Dunkl operators (rational)      190 277
Dunkl operators (trig)      75 121 275
Dunkl operators (universal)      415
Eigenvectors v(X, Y)      343
Elliptic Weyl group ($GL_n$)      101
Evaluation formula      98 100 206
Evaluation formula (DAHA)      317 319
Evaluation map ($A_1$)      96 200
Expectation value $\{H\}_0\:(A_1)$      95
Extended Weyl group      112 262 295
Factorized KM algebra ($\hat\mathfrak g$)      132
Factorizing subalgebra $\tilde\mathfrak g_r$      132
Fourier transform $\psi_0$ (skew)      328
Fourier transform $\varphi_0$      328
Fourier transform E ($A_1$)      213
Fourier transform S ($A_1$)      213
Fourier transforms $\bar{\mathbf S}, \, \bar{\mathbf E}$ ($A_1$)      223
Fourier transforms $\bar{\phi_0}$, $\bar{\psi_0}$      330
Fourier — Jackson transform $\psi_0$      335
Fourier — Jackson transform $\varphi_0$      335
Functional representation      326 383
Gaudin model      151
Gaussian $\gamma$      233 331
Gaussian $\gamma$ (restricted)      393
Gaussian sum $\tau$ (generalized)      163
H: nonaffine Hecke      308 383 409
Hankel transform      186 188 194
Hankel transform $\mathbf H_{re, im}$      162
Harish — Chandra function $\sigma$      122
Harish — Chandra transform      116
Hecke algebra $\mathbf H_n$      100 359 367
Hecke algebra H      308 383 409
Heckman — Opdam operators $L'_p$      123
Hypergeometric function      123
Induced module $I_\lambda$ ($\mathcal H'_\Sigma$)      57
Induced module $\mathcal I_X[\xi]$ (DAHA)      344
Intermediate subalgebras $\mathcal{HH}^\flat$      311
Intertwiners $f_w$ (degenerate)      58
Intertwiners $F_w(u)$ (affine, $GL_n$)      78
Intertwiners $\Phi_{\hat w}$ (DAHA)      320 321
Intertwiners $\Psi'_{\hat w}$ (degenerate)      120
Intertwiners normalized      274 320
Intertwining operator $\Pi$ ($A_1$)      205
Invariance (AKZ, $\mathbb S_n$)      52
Invariance (AKZ, W)      54
Invariance (QAKZ, W)      78
Invariant form ($\star$-invariant)      345
Invariant module ($PGL^c(2, \mathbb Z)$)      392
Invariants v (DAHA)      371 372
Inverse order in $\delta$      359
Inversion $\mathcal H'$      125
Inversion ($A_1$)      162 189 224
Inversion (DAHA)      268 337—339
Inversion {$A_1$, truncated)      194
Involution $r\mapsto r^*$      271
Involution $\eta$      202 308
Involution $\varepsilon$      213 272 307
Jackson master formula      224
Jackson sum      176 334
Jucys — Murphy generators      67
k-function      108 306
Kazhdan — Lusztig involution      202 308
Kodaira — Spencer map      35 220
KZ (r-matrix)      135
Length $l(\hat w)$      119 262 296
Little Verlinde algebra      260
Lusztig map      276 278
Macdonald operators      84 316
Macdonald polynomials $P_b$      316
Macdonald polynomials $p_\lambda$      99
Macdonald problem      84
Maximal root $\theta$      118
Maximal short root $\vartheta$      262 295
Mehta — Macdonald intg      289 332
Mellin transform $\Psi$      171 174
Monodromy (AKZ)      62 69
Monodromy cocycle (QAKZ)      81
Monomial functions      316
New points (integral formulas)      142
Noncompact case      165
Nonsymmetric polynomials $E_b$      314
Nonsymmetric polynomials $e_n$      197
Nonsymmetric Verlinde algebra      248
Norm formula      206 325 330
Old points (integral formulas)      142
Opdam transform $\mathcal F$      124
Opdam transform $\mathcal G$ (inverse)      125
P: weight lattice      1—417
Pair $\{\Delta, C\}$      359
Pair $\{\Delta, C\}$ (generalized)      369
Pair $\{\Delta, C\}$ (new)      363
Pairs $\{\Delta, C\}$ (equivalent)      364
Partition increasing      362
Partition of $\delta$      362
Partition of $\delta$ new      363
Partition ordered      363
Perfect module (DAHA)      399
Perfect representation ($A_1$)      248
Pieri formula ($A_1$)      97 98 206
Pieri formula ($GL_n$)      99
Plancherel $A_1$      190 194 221
Plancherel $\mathcal{HH}$      268 336—338
Polynomial rep      273 310 372
Polynomial rep $A_1$      96 190
Polynomial rep (rational)      277
Primitive module (DAHA)      373
Primitive weight $xi_0$      382 386 388
Principal module (DAHA)      373
Principal-special ($A_1$)      238
Pseudo-hermitian form      345
Pseudo-unitary module      248 345
Q: root lattice      1—417
QMBP      60 74
Quadratic relations (Hecke)      77
Quantum many-body problem      60
R, r: r-matrices      1—153
r-matrix (extension of)      108
r-matrix (invariant)      108
r-matrix (unitary)      131 140
R: root system      281^117
Radial part $L^{(k)}$ ($SO_2$)      92
Range $\ddot\Upsilon_+[\xi]$ (boundary)      346
Range $\Upsilon_*[\xi]$ (semisimple)      347
Range $\Upsilon_+[-\rho_k]$ (sharp)      348
Range $\Upsilon_+[\xi]$ (plus)      346
Range $\Upsilon_0[\xi]$ (zero)      347
Range $\Upsilon_{-}[\xi]$ (minus)      347
Reflection $r\mapsto r^*$      271
Restricted category      287
Rho $\rho$      294 306
Rogers polynomials $p_n$      93 195
Root (extreme, $\eta$-identities)      339
r—matrix (afnne)      112
Self-consistent (AKZ)      54
Self-dual module (DAHA)      392
Semi-classical limit (QAKZ)      79
Semisimple module (X, Y)      345
Shift formula      189
Shift operator S      171
Skew diagram      358
Skew paths in $\delta$      361
Spectrum (X, Y)      345
Spherical irrep ($A_1$)      248
Spherical module (DAHA)      371
Spherical polynomials $\mathcal E_b$      317
Spherical rep $\Delta^+$      263
Spherical vectors      371 372
Stabilizer $\hat W^\flat[\xi]$      343 347
Standard invariant form (fl)      130
Standard roots $\alpha, \beta$      106
Standard subsystem (rk=2)      108
Subdiagram basic      360
Subdiagram fundamental      361
Subdiagram of $\delta$      360
Subpair fundamental      363
Subpairs equivalent      365
Sugawara elements $L_{-1}^i$      139
Symmetrizer      263
Trace on $\J_\lambda$      72
Truncated $\theta$-function      169 316
Ultraspherical polynomials      93
Unitary automorphism      308
Unitary module for X, Y      345 346
Vacuum vector      141
Verlinde algebra ($A_1$)      248
Verlinde algebra (DAHA)      403
Verlinde algebra (little)      260
Verma module      46
Weights $\xi$ (GL)      359
Weights $\xi$ (X, Y)      343
Well-ordered diagram      143
Weyl group W      53 293
Weyl module $M_V$ ($\mathfrak g$)      138
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте